LAUSR

Abstract Direct numerical simulations of supersonic flows past a two-dimensional cavity with a length-to-depth ratio of 4 under different Mach numbers are performed. Firstly, as the Mach number increased from 1.1 to 2.7 with a small initial boundary layer thickness, the dominant flow mode transforms from a wake mode to the Rossiter II mode, and to the Rossiter III mode, then to a steady mode. Meanwhile, a low frequency mode appears, and then disappears due to the change of vortex-corner interactions. With a sufficiently large initial boundary layer thickness, the wake mode is not obtained, and the dominant flow mode will change from the Rossiter II mode to the steady mode directly. Secondly, in the shear layer mode, the local sound pressure level for the dominant mode and the overall sound pressure level distributions on the cavity floor show reduced pressure oscillations with increased Mach number due to the weakened shear layer instability. Thirdly, the variation of the vortex structures is more complex, and pressure oscillations have a stronger impact on the mean flow in the wake mode, comparing with the shear layer mode. Finally, a dynamic mode decomposition approach is performed to obtain dynamic information. The oscillation frequencies obtained from the dynamic mode decomposition are consistent with the results of local power spectral density analysis, and the dominant mode transition is detected by the dynamic modes obtained from the dynamic mode decomposition.